Chapter 11: Problem 22
Solve the proportion. Check for extraneous solutions. $$\frac{24}{5}=\frac{9}{y+2}$$
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When you add rational expressions, you may need to factor a trinomial to find the LCD. Study the sample below. Then simplify the expressions in Exercises 46–49. $$\text { Sample: } \frac{2 x}{x^{2}-1}+\frac{3}{x^{2}+x-2}=\frac{2 x}{(x+1)(x-1)}+\frac{3}{(x-1)(x+2)}$$ The LCD is \((x+1)(x-1)(x+2)\) Note: If you just used \(\left(x^{2}-1\right)\left(x^{2}+x-2\right)\) as the common denominator, the factor \((x-1)\) would be included twice. $$\frac{7 x+2}{16-x^{2}}+\frac{7}{x-4}$$
A contestant on a television game show must guess the price of a trip within 1000 dollars of the actual price in order to win. The actual price of the trip is 8500 dollars .Write an absolute-value inequality that shows the range of possible guesses that will win the trip. (Review 6.4 )
Evaluate the function for \(x=0,1,2,3,\) and 4. $$f(x)=-x^{2}$$
Evaluate the expression. $$2^{4} \cdot 2^{3}$$
Completely factor the expression. $$5 x^{2}-51 x+54$$
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